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Locally stationary Hawkes processes
- François Roueff
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- References
- ISNPS, Avignon, June 2016,
- Abstract
We introduce non-stationary Hawkes processes which are defined
similarly to standard Hawkes processes but with a time- (or space-)evolving
base intensity and fertility function. The resulting process is
inhomogeneous. However the usual conditions for the existence of a stationary
Hawkes process are easily adapted to obtain a stable non-stationary model. A
wildly non-stationary model cannot be consistently inferred, even from an
infinite sample of data. Having in mind the statistical analysis of
non-stationary Hawkes processes, we propose an approach inspired from locally
stationary time series. We are thus interested in an asymptotic framework
where the dimension of the observation windows tend to infinity while the
time- (or space-)varying parameters are sampled from a function whose
corresponding support remains unchanged. We show that under simple
assumptions, the statistical properties of the locally stationary Hawkes
process can be approximated by those of a stationary Hawkes process. In
particular, this framework allows us to propose a time-frequency analysis of
Hawkes processes with time varying parameters.
- Keywords
- Category
- Invited speaker to a conference
- Research Area(s)
- Computer Science/Signal and Image Processing
Statistics/Applications
Statistics/Methodology
- Identifier(s)
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Bibliographic key isnps-2016-roueff
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- Last update
- on september 05, 2017 by Francois Roueff
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